DescriptionMulti-input and multi-output (MIMO) radars achieve high resolution of arrival direction by transmitting orthogonal waveforms, performing matched filtering at the receiver end and then jointly processing the measurements of all receive antennas. This dissertation studies the use of compressive sensing (CS) and matrix completion (MC) techniques as means of reducing the amount of data that need to be collected by a MIMO radar system, without sacrificing the system’s good resolution properties. MIMO radars with sparse sensing are useful in networked radar scenarios, in which the joint processing of the measurements is done at a fusion center, which might be connected to the receive antennas via a wireless link. In such scenarios, reduced amount of data translates into bandwidth and power saving in the receiver-fusion center link. First, we consider previously defined CS-based MIMO radar schemes, and propose optimal transmit antenna power allocation and transmit waveform design schemes that improve target localization performance. The optimization criterion is to minimize the coherence between the columns of the sensing matrix. In addition, we propose a clutter suppression scheme based on the Capon beamforming in the CS-based MIMO radars. Second, we propose a novel MIMO radar approach based on matrix completion, termed as MIMO-MC, in which each receive node either performs matched filtering with a small number of randomly selected dictionary waveforms, or obtains sub-Nyquist samples of the received target echoes at randomly sampled instants, and forwards the results to a fusion center. Based on the received samples, and with knowledge of the sampling scheme, the fusion center partially fills a matrix, referred to as the data matrix and subsequently applies matrix completion techniques to estimate the full matrix. The completed data matrix is used for target estimation with standard array signal processing methods. We show that MIMO-MC radars share the advantages of the CS based radars, i.e., high resolution with reduced amounts of data, but unlike CS-based radars do not require grid discretization and thus are not sensitive to basis mismatch. For MIMO radars with uniform linear arrays, we investigate the relationship between the coherence of the data matrix and the transmit waveforms, and formulate an optimal waveform design problem. This is an optimization problem on the complex Stiefel manifold, which is then solved via the modified steepest descent and the modified Newton algorithms with nonmonotone line search methods. We also propose transmit and receive beamforming schemes to significantly reduce the sampling rate at the receiver end in MIMO-MC radars.